Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 4 3 2016 7 29 Some new Formulas for the Kolakoski Sequence A000002 54 59 EN Abdallah Hammam Département de Mathématiques et Informatique, Université Moulay Ismaїl Faculté des sciences, Meknès, Morocco TJANT2016431 10.12691/tjant-4-3-1 2016 3 13 2016 6 20 2016 7 27 We present here two formulas for the Kolakoski sequence (Kn)n1. The first one is in concern with the frequency of the letters 1 and 2 in this sequence. Our investigation seems to support the hypothesis of the Keane's conjecture. In the second part of this paper, we give an expression of the nth term of the sequence, Kn, according to K1,K2,...Kp, with improving so, the former known value given by Bordellès [2].